Abstract

It is well known that front interfaces in bistable isotropic reaction-diffusion equations are asymptotically stationary or move with constant speed. It has been numerically observed that self-organised front motion by interacting components occurs in multi-component reaction-diffusion system with one fast component governed by an Allen-Cahn equation that is coupled to slow linear equations. Here we consider general number of additional components and rigorously study existence, stability and bifurcations of stationary and uniformly travelling front solutions near the singular limit. Combining an Evans function and a functional analytic approach we find that the organising center for the dynamics of front speeds yields an N-th order ODE for N additional components. Analysing the normal form, for N = 3 we prove that chaotic dynamics occurs in the sense of an unfolded Shil'nikov homoclinic orbit. Numerical study guided by our analytic findings complement these results.

This is joint work with Martina Chirilus-Bruckner (Leiden) and Peter van Heijster (Wageningen).

 

WebEx Link: TBA 

 

Organizers: Chueh-Hsin Chang (CCU), Jia-Yuan Dai (NTHU), Bo-Chih Huang (CCU), Chih-Chiang Huang (CCU), Alejandro López-Nieto (NTU), Chang-Hong Wu (NYCU)